So in UK toilet, loo bog etc. But how do Americans differentiate from a room with just a toilet bowl and sink and one with a bath / shower as well? Just curious.
In most homes in the US the bathroom includes the toilet, the sink, the tub, and the shower. There is no separation of rooms. But in some cases there are rooms that include just the toilet and sink. It's can be called bathroom, a 1/2 bath, or Powder Room. It’s usually located on the first floor by the foyer.

